Mathematical Prediction of the Dysmetric Dimension: A4. Abstract Dysmetric form of Physical Laws

Having developed the foundations of Dyadic Algebra of Magnitudes, Dysmetric Spaces, and Differential Dysmetry in the preceding articles, we synthesize here the application of that purely mathematical knowledge to the extension of any physical law towards its corresponding dysmetric formulation. To this end, we always take a physical law as reference and theoretically activate dysmetry to analyze how its formulation is modified in each case. We do not question the validity of the current laws, but extend them through the abstract application of the dysmetric effect. This leads to formulations that reduce to the existing laws when the dysmetry disappears. We identify, whenever possible, the dysmetric component, which determines in what type of dysmetric spaces the parent law remains invariant. We also show that the dysmetric form reduces to the original law when all dysmetric densities of all magnitudes are constant and equal to unity. This procedure leads us to observe that operating with magnitudes without a well-constructed algebra of their own restricts the phenomena considered to isometric ones. Conversely, when quantities of magnitudes are endowed with their dyadic algebra, dysmetry and its infinite breadth become apparent, allowing the framework to encompass phenomena that are not isometric. In this way, any law expands its meaning and validity, adopting a new form of abstract mathematics that allows it to be adapted flexibly to the experimental observations we wish to represent.